Shear bands are common in dense quasi-static granular flows. They can appear in the interior of the flowing material or at confining boundaries and are typically of the order of ten particle diameters in thickness. Deformation tends to be localized in shear bands separating non-deforming or weakly deforming regions. Dilatancy and sharp velocity variation are typical in these shear layers. Much work has been reported in the literature concerning the development of non-local quasi-static rheological models to predict the flow behaviour in shear layers. In a recent article, Dsouza & Nott ( J. Fluid Mech. , vol. 888, 2020, R3) derive a non-local extension to a classical plasticity model by postulating that some local quantities appearing in the yield function, which stipulates the relationship between different components of the stress for the material to undergo sustained yielding, and the flow rule which provides information on the rate of deformation tensor to within an arbitrary multiplicative constant, should be replaced by their local averages. They then obtain an explicit non-local model which does not involve new microstructural variables and they show that the model captures velocity and volume fraction fields in simple shear flows, although some model parameters must be fitted to achieve quantitative agreement. This article discusses the work of Dsouza & Nott (2020) and comments on work ahead for further testing and developing the model.

中文翻译：

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模拟致密颗粒流中的剪切层

剪切带在密集的准静态颗粒流中很常见。它们可以出现在流动材料的内部或限制边界处，通常厚度约为 10 个颗粒直径。变形往往集中在分隔非变形或弱变形区域的剪切带中。在这些剪切层中，剪胀和急剧的速度变化是典型的。关于开发非局部准静态流变模型来预测剪切层中的流动行为，文献中已经报道了很多工作。在最近的一篇文章中，Dsouza & Nott (J. Fluid Mech., vol. 888, 2020, R3) 通过假设一些局部量出现在屈服函数中，推导出经典塑性模型的非局部扩展，规定了材料承受持续屈服应力的不同分量之间的关系，以及提供变形张量速率信息的流动规则，应由它们的局部平均值代替。然后他们获得了一个明确的非局部模型，该模型不涉及新的微观结构变量，并且他们表明该模型捕获了简单剪切流中的速度和体积分数场，尽管必须拟合一些模型参数才能实现定量一致。本文讨论了 Dsouza & Nott (2020) 的工作，并对未来进一步测试和开发模型的工作进行了评论。提供变形张量在任意乘法常数内的速率信息的流动规则应该由它们的局部平均值代替。然后他们获得了一个明确的非局部模型，该模型不涉及新的微观结构变量，并且他们表明该模型捕获了简单剪切流中的速度和体积分数场，尽管必须拟合一些模型参数才能实现定量一致。本文讨论了 Dsouza & Nott (2020) 的工作，并对未来进一步测试和开发模型的工作进行了评论。提供变形张量在任意乘法常数内的速率信息的流动规则应该由它们的局部平均值代替。然后他们获得了一个明确的非局部模型，该模型不涉及新的微观结构变量，并且他们表明该模型捕获了简单剪切流中的速度和体积分数场，尽管必须拟合一些模型参数才能实现定量一致。本文讨论了 Dsouza & Nott (2020) 的工作，并对未来进一步测试和开发模型的工作进行了评论。尽管必须拟合一些模型参数才能达到定量一致。本文讨论了 Dsouza & Nott (2020) 的工作，并对未来进一步测试和开发模型的工作进行了评论。尽管必须拟合一些模型参数才能达到定量一致。本文讨论了 Dsouza & Nott (2020) 的工作，并对未来进一步测试和开发模型的工作进行了评论。